i$)$ A $24\mathrm{.}0kg$ solid disk with a radius of $1\mathrm{.}20m$ is rotating at $220re\frac{v}{m}in.$ It must be brought to a stop in $12\mathrm{.}0s.$ Calculate the required angular acceleration. Calculate the magnitude of the corresponding force if it is to be applied tangentially at the rim.

ii$)$ Suppose that a simple pendulum consists of a small $80\mathrm{.}0g$ bob at the end of a cord of negligible mass. The angle between the cord and the vertical varies according to

$=(0\mathrm{.}1600$rad$)cos[(2\mathrm{.}22\frac{\text{r}\text{a}\text{d}}{s})t+]$

Calculate the pendulum's length and its maximum kinetic energy.